Refinement of Ostrowski inequality and functions of bounded variation on new f-divergence measure with applications

Nidhi Sharma; RAM NARESH SARASWAT

doi:10.5269/bspm.78344

Nidhi Sharma Manipal University Jaipur
RAM NARESH SARASWAT Manipal University Jaipur

Résumé

Information Inequalities prove to be a powerful tool to quantify uncertainties and data dependencies. They provide useful insights into the relations between information-theoretic probability distributions. The entropy and divergence measure makes the data processing inequalities more effective for communication and informatic concepts. This study provides the constructive perspective of Ostrowski type inequality for functions of bounded variation. Explored approximation of new f divergence measure by applying principles of numerical integration theory. Discussed function f and its first derivatives exhibit bounded variation characteristics. Furthermore, by applying the bounded variation properties of the function f and its derivatives, accurate and efficient approximations can be achieved. Additionally, we have found applications of the obtained information inequalities related to the Relative Arithmetic-Geometric Divergence (AGD) that quantify the difference between probability distributions. Some identified means are also used to specify the results.

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